Why do the output colours differ from the input when using Filmic Blender in the VSE?
Your understanding is incorrect. Filmic  blender does not scan the image to find high and low values. It does not normalize the image. There is a so-called "tutorial" out there that is spreading wrong information. 

Filmic blender works with with fixed parameters. Data within those parameters gets mapped to display referred values. Unless you feed images that are in scene referred values and within the range used by filmic blender, it makes no sense to use filmic blender's transforms for the VSE.

Even if you where to linearize display referred images, you would need to bring the scene referred values to the proper range to use of filmic blender's transforms. Most images imported into blender get linearized to display linear values (0 to 1). Filmic blender works on values much larger than 1, white would be around 16.9 in scene referred values.

Your images would need to be linear EXR files (with scene referred values in the range used by filmic blender) or they would need to be log encoded, to be linearized using the proper transform to fall within the range used by filmic blender. 

Please read the following link to learn more about filmic blender:

Render with a wider dynamic range in cycles to produce photorealistic looking images